%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:09:09 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 9 unt; 2 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 85 ( 33 ~; 28 |; 17 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X] :
( inductive(X)
<=> ( subclass(image(successor_relation,X),X)
& member(null_class,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
? [X] :
( ! [Y] :
( inductive(Y)
=> subclass(X,Y) )
& inductive(X)
& member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ member(null_class,universal_class),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,Y)
| ~ member(U,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f47,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
( ! [X,Y] :
( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ! [X,Y] :
( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [X,Y] :
( ( ~ member(sK0_skl(Y,X),Y)
& member(sK0_skl(Y,X),X) )
| subclass(X,Y) )
& ! [X,Y] :
( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(U,sK0_skl(Y,X))],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f130,plain,
! [X] :
( ( ~ subclass(image(successor_relation,X),X)
| ~ member(null_class,X)
| inductive(X) )
& ( ( subclass(image(successor_relation,X),X)
& member(null_class,X) )
| ~ inductive(X) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f131,plain,
( ! [X] :
( ~ subclass(image(successor_relation,X),X)
| ~ member(null_class,X)
| inductive(X) )
& ! [X] :
( ( subclass(image(successor_relation,X),X)
& member(null_class,X) )
| ~ inductive(X) ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f135,plain,
? [X] :
( ! [Y] :
( subclass(X,Y)
| ~ inductive(Y) )
& inductive(X)
& member(X,universal_class) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f136,plain,
( ! [Y] :
( subclass(sK1_skl,Y)
| ~ inductive(Y) )
& inductive(sK1_skl)
& member(sK1_skl,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X,sK1_skl)],[f135]) ).
fof(f138,plain,
inductive(sK1_skl),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f191,plain,
~ member(null_class,universal_class),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f199,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f53,f50]) ).
fof(f209,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,universal_class) ),
inference(resolution,[status(thm)],[f199,f132]) ).
fof(f213,definition,
( sQ0_spl
<=> member(null_class,universal_class) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ0_spl
| member(null_class,universal_class) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
! [X0] :
( sQ1_spl
<=> ~ inductive(X0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f217,plain,
! [X0] :
( ~ sQ1_spl
| ~ inductive(X0) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f209,f213,f216]) ).
fof(f220,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f191]) ).
fof(f221,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f138,f217]) ).
fof(f223,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f224,plain,
$false,
inference(sat_refutation,[status(thm)],[f219,f221,f223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:50:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.052927 seconds
% 0.09/0.42 % CPU time: 0.138361 seconds
% 0.09/0.42 % Total memory used: 75.193 MB
% 0.09/0.42 % Net memory used: 75.128 MB
%------------------------------------------------------------------------------